8th Grade Mathematics Curriculum · 8th Grade Mathematics Curriculum. Course Summary: In Grade 8,...
Transcript of 8th Grade Mathematics Curriculum · 8th Grade Mathematics Curriculum. Course Summary: In Grade 8,...
8th Grade Mathematics Curriculum Course Summary: In Grade 8, instructional time will focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling and association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem. Scope and Sequence:
Time Frame Unit
34 Days Number Sense, Expressions, and Equations
68 Days Functions and Linear Relationships
27 Days Transformations and Transversals
35 Days Exponential Functions, Pythagorean Theorem, and Volume
Board Approved: July 23, 2015 2 | Page Revised: April, 2016 MLS Alignment: April, 2017
Curriculum Revision Tracking
Changes made in April, 2016:
● Unit 1: o Pacing was adjusted from 32 to 34 days o Sequence of Topics 6, 14, and 15 was changed.
Board Approved: July 23, 2015 3 | Page Revised: April, 2016 MLS Alignment: April, 2017
Unit 1: Number Sense, Expressions and Equations
Subject: Mathematics Grade: 8th Grade Name of Unit: Number Sense, Expressions, and Equations Length of Unit: 34 days Overview of Unit: Students will understand that there are numbers which are not rational and approximate them by rational numbers. Students will also analyze and solve linear equations. Priority Standards for unit:
• MA.8.NS.A.1: Explore the real number system. a. Know the differences between rational and irrational numbers. b. Understand that all rational numbers have a decimal expansion that terminates or
repeats. c. Convert decimals which repeat into fractions and fractions into repeating
decimals. d. Generate equivalent representations of rational numbers.
Supporting Standards for unit:
● MA.8.NS.A.2: Estimate the value and compare the size of irrational numbers and approximate their locations on a number line. For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
● MA.8.EEI.C.1: Solve linear equations and inequalities in one variable. a. Create and identify linear equations with one solution, infinitely many solutions
or no solutions. b. Solve linear equations and inequalities with rational number coefficients,
including equations and inequalities whose solutions require expanding expressions using the distributive property and combining like terms.
● ISTE-EMPOWERED LEARNER 1: Students leverage technology to take an active role in choosing, achieving and demonstrating competency in their learning goals, informed by the learning sciences.
● ISTE-KNOWLEDGE COLLECTOR.3: Students critically curate a variety of resources using digital tools to construct knowledge, produce creative artifacts and make meaningful learning experiences for themselves and others.
● ISTE-INNOVATIVE DESIGNER.4: Students use a variety of technologies within a design process to identify and solve problems by creating new, useful or imaginative solutions.
● ISTE-COMPUTATIONAL THINKER.5: Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions.
Board Approved: July 23, 2015 4 | Page Revised: April, 2016 MLS Alignment: April, 2017
Standard Unwrapped Concepts (Students
need to know)
Unwrapped Skills (Students need to
be able to do)
Bloom’s Taxonomy
Levels Webb's DOK
MA.8.NS.A.1 differences between rational and
irrational numbers. Know Remember 1
MA.8.NS.A.1
all rational numbers have a decimal expansion that terminates
or repeats. Understand Understand 2
MA.8.NS.A.1
decimals which repeat into fractions and fractions into
repeating decimals Convert Apply 2
MA.8.NS.A.1 equivalent representations of
rational numbers Generate Create 2 Essential Questions:
1. In earlier courses you studied rational numbers. What other types of numbers are there? 2. In earlier courses you studied rational numbers. Why do you need them? 3. Why do you write equations?
Enduring Understanding/Big Ideas:
1. There are rational and irrational numbers in the real number system. 2. Know the differences between them can help you understand if a fraction can be made
from the number, or whether or not a decimal and be derived from a fraction or square roots.
3. Complex questions can be solved using the structure of an equation and the process of inverse operations to isolate variables.
Unit Vocabulary:
Academic Cross-Curricular Words Content/Domain Specific
Ratios
Percents
Topic 1 Irrational Numbers
Perfect Square Real Number
Repeating Decimal Square Root
Terminating Decimal
Resources for Vocabulary Development: Use quality tools (See Adult Learning Framework handbook)
Board Approved: July 23, 2015 5 | Page Revised: April, 2016 MLS Alignment: April, 2017
digits Topic 1: Rational & Irrational Numbers
Standard Topic & Section Suggested # of Days
Notes
MA.8.NS.A.1 1.1: Expressing Rational Numbers and Decimal Expansion
1
MA.8.NS.A.1 1.2: Exploring Rational Numbers 1
MA.8.NS.A.1 1.3: Approximating Rational Numbers
1
MA.8.NS.A.2 1.4: Comparing and Ordering Rational and Irrational Numbers
1
MA.8.NS.A.1 MA.8.NS.A.2
1.5: Problem Solving 1
Review Day 1.5 Review, Look Over and Test within a three day period (suggested) Test 1.5
Board Approved: July 23, 2015 6 | Page Revised: April, 2016 MLS Alignment: April, 2017
digits Topic 2: Linear Equations in One Variable
Standard Topic & Section Suggested # of Days
Notes
Add/Subtract/Multiply/Divide Integers
2 Supplement Algebra 2.5 and 2.6
as needed
Intervention Clusters 10, 11 and 12.1 “Fractions”
Approx. 4 as needed
Use Intervention Lessons, Journal Entries and Intervention
HW assignments as needed
Supplement Distributive Property
1 Supplement May need to create own practice
Supplement Simplifying Expressions (Combining Like Terms)
1 Supplement May need to create own practice
Intervention Cluster 25 “Expressions and Equations”
Approx. 4 as needed
Use Intervention Lessons, Journal Entries and Intervention
HW assignments as needed
MA.7.EEI.B.1 2.1: Solving Two-Step Equations 1 Algebra 3.1 - 3.4
MA.7.EEI.B.1 2.2: Solving Equations with Variables on Both Sides
1 Algebra 3.1 - 3.4
MA.7.EEI.B.2 2.3: Solving Equations Using the Distributive Property
1 Algebra 3.1 - 3.4
REVIEW Solving Equations 1
Quiz Solving Equations 1
MA.7.EEI.B.2 2.4: Solutions - One, None, or Infinitely Many
1
MA.7.EEI.B.2 2.5: Problem Solving 1
Review Topic 2 1.5
Test Topic 2 1.5
Board Approved: July 23, 2015 7 | Page Revised: April, 2016 MLS Alignment: April, 2017
Unit 2: Functions and Linear Relationships
Subject: Mathematics Grade: 8th Grade Name of Unit: Functions and Linear Relationships Length of Unit: 68 Days Overview of Unit: Students will understand the concepts related to identifying, creating, manipulating and solving functions and systems of equations. Students will also understand the concepts of using and creating systems of categorical data. Priority Standards for unit:
● 8.EEI.B.1: Graph proportional relationships. a. Interpret the unit rate as the slope of the graph. b. Compare two different proportional relationships.
For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
● 8.EEI.B.2: Apply concepts of slope and y-intercept to graphs, equations and proportional relationships.
a. Explain why the slope (m) is the same between any two distinct points on a non-vertical line in the Cartesian coordinate plane.
b. Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
● 8.EEI.C.1: Solve linear equations and inequalities in one variable. a. Create and identify linear equations with one solution, infinitely many
solutions or no solutions. b. Solve linear equations and inequalities with rational number coefficients,
including equations and inequalities whose solutions require expanding expressions using the distributive property and combining like terms.
● 8.EEI.C.2: Analyze and solve systems of linear equations. a. Graph systems of linear equations and recognize the intersection as the
solution to the system. b. Explain why solution(s) to a system of two linear equations in two variables
correspond to point(s) of intersection of the graphs. c. Explain why systems of linear equations can have one solution, no solution or
infinitely many solutions. d. Solve systems of two linear equations.
● 8.F.A.3: Investigate the differences between linear and nonlinear functions. a. Interpret the equation y = mx + b as defining a linear function, whose
parameters are the slope (m) and the y-intercept (b). b. Recognize that the graph of a linear function has a constant rate of change c. Give examples of nonlinear functions.
Board Approved: July 23, 2015 8 | Page Revised: April, 2016 MLS Alignment: April, 2017
Supporting Standards for unit: ● 8.EE.6. Use similar triangles to explain why the slope m is the same between any two
distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
● 8.EE.7 Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
● 8.DSP.A.1: Construct and interpret scatter plots of bivariate measurement data to investigate patterns of association between two quantities.
● 8.DSP.A.2: Generate and use a trend line for bivariate data, and informally assess the fit of the line.
● 8.DSP.A.3: Interpret the parameters of a linear model of bivariate measurement data to solve problems.
● 8.DSP.A.4: Understand the patterns of association in bivariate categorical data displayed in a two-way table.
a. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.
b. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.
● 8.F.A.1: Explore the concept of functions. (The use of function notation is not required.) a. Understand that a function assigns to each input exactly one output. b. Determine if a relation is a function. c. Graph a function.
● 8.F.A.2: Compare characteristics of two functions each represented in a different way. ● 8.F.B.1: Use functions to model linear relationships between quantities.
a. Explain the parameters of a linear function based on the context of a problem. b. Determine the parameters of a linear function. c. Determine the x-intercept of a linear function.
● 8.F.B.2: Describe the functional relationship between two quantities from a graph or a verbal description.
● ISTE-EMPOWERED LEARNER 1: Students leverage technology to take an active role in choosing, achieving and demonstrating competency in their learning goals, informed by the learning sciences.
Board Approved: July 23, 2015 9 | Page Revised: April, 2016 MLS Alignment: April, 2017
Standard Unwrapped Concepts
(Students need to know)
Unwrapped Skills (Students need to
be able to do)
Bloom’s Taxonomy
Levels Webb's DOK
8.EEI.B.1 Proportional relationships Graph Apply 2
8.EEI.B.1 Unit rate as the slope of the
graph Interpret Understand 2
8.EEI.B.1 Two different proportional
relationships Compare Analyze 2
8.EEI.B.2
Concepts of slope and y-intercept to graphs, equations and proportional relationships
Apply Apply 2
8.EEI.B.2
why the slope (m) is the same between any distinct points on a non-vertical line in the Cartesian
coordinate plane. Explain Understand 3
8.EEI.B.2
the equation y = mx for a line through the origin and the
equation y = mx + b for a line intercepting the vertical axis at b. Derive Create 2
8.EEI.C.1 Systems linear equations in and
inequalities in one variable Solve Apply 2
8.EEI.C.1
linear equations with one solution, infinitely many solutions or no solution Create Create 3
8.EEI.C.1
linear equations with one solution, infinitely many solutions or no solution Identify Remember 1
8.EEI.C.1
linear equations and inequalities with rational number
coefficients, including equations and inequalities whose solutions require expanding expressions using the distributive property
and combining like terms Solve Apply 2 8.EEI.C.2 Systems of Linear Equations Analyze Analyze 2 8.EEI.C.2 Systems of Linear Equations Solve Apply 2
8.EEI.C.2
systems of linear equations and recognize the intersection as the
solution to the system. Graph Apply 2
Board Approved: July 23, 2015 10 | Page Revised: April, 2016 MLS Alignment: April, 2017
8.EEI.C.2
why solution(s) to a system of two linear equations in two
variables correspond to point(s) of intersection of the graphs Explain Understand 3
8.EEI.C.2
why systems of linear equations can have one solution, no solution or infinitely many
solutions. Explain Understand 3 8.EEI.C.2 systems of two linear equations Solve Apply 2
8.F.A.3 the differences between linear
and nonlinear functions. Investigate Understand 1
8.F.A.3
the equation y = mx + b as defining a linear function, whose parameters are the slope (m) and
the y-intercept (b). Interpret Analyze 2
8.F.A.3 that the graph of a linear function
has a constant rate of change Recognize Understand 1 8.F.A.3 examples of nonlinear functions. Give Understand 2
8.DSP.A.1
scatter plots of bivariate measurement data to investigate patterns of association between
two quantities. Construct Apply 2
8.DSP.A.1
scatter plots of bivariate measurement data to investigate patterns of association between
two quantities. Interpret Analyze 3
8.DSP.A.2
trend line for bivariate data, and informally assess the fit of the
line. Generate Create 2
8.DSP.A.2
trend line for bivariate data, and informally assess the fit of the
line. Use Understand 2
8.DSP.A.3
parameters of a linear model of bivariate measurement data to
solve problems. Interpret Understand 2
8.DSP.A.4
patterns of association in bivariate categorical data
displayed in a two-way table. Understand Understand 2
8.DSP.A.4
two-way table summarizing data on two categorical variables
collected from the same subjects. Construct Create 2 8.DSP.A.4 two-way table summarizing data Interpret Analyze 2
Board Approved: July 23, 2015 11 | Page Revised: April, 2016 MLS Alignment: April, 2017
on two categorical variables collected from the same subjects.
8.DSP.A.4
relative frequencies calculated for rows or columns to describe possible association between the
two variables. Use Understand 2 8.F.A.1 the concept of functions Explore Evaluate 3
8.F.A.1 a function assigns to each input
exactly one output Understand Understand 1
8.F.A.1 if a relation is a function Determine
Understand 2 8.F.A.1 a function Graph Apply 2
8.F.A.2
characteristics of two functions each represented in a different
way. Compare Analyze 3
8.F.B.1 functions to model linear
relationships between quantities. Use Understand 3
8.F.B.1
the parameters of a linear function based on the context of
a problem Explain Understand 3
8.F.B.1 the parameters of a linear
function Determine Understand 2
8.F.B.1 the x-intercept of a linear
function Determine Understand 3
8.F.B.2
the functional relationship between two quantities from a graph or a verbal description. Describe Evaluate 3
Essential Questions:
1. What is a function? How are functions used? Enduring Understanding/Big Ideas:
1. A function is a relationship between x and y, such that for every x input there is one and only one y output. Functions are used to describe and predict relationships between bivariate sets of data.
Unit Vocabulary:
Academic Cross-Curricular Words Content/Domain Specific
Scatter Plot Initial Values
Topic 7 Function
Board Approved: July 23, 2015 12 | Page Revised: April, 2016 MLS Alignment: April, 2017
Trend Line Outlier Cluster
Bivariate Data
Independent Variable Dependent Variable
Experiment Group
Control Group
Relationship
Linear Function Non-Linear Function
Interval Rate of Change
Relation Vertical Line Test
Topic 5
Linear Equation Slope
Slope of a line y-intercept
Proportional Relationship Rate of Change
Topic 8 Linear Function Rule
Initial Value Unit Rate
Topic 14 Cluster
Gap Outlier
Scatter Plot Trend Line
Positive or Negative Association Linear or Nonlinear Association
Topic 6
Solution of a System of Linear Equations System of Linear Equations
Topic 15
Bivariate Categorical Data Bivariate Data
Categorical Data Measurement Data
Two-way Frequency Table Two-way Relative Frequency Table
Resources for Vocabulary Development: Use quality tools (See Adult Learning Framework handbook)
Board Approved: July 23, 2015 13 | Page Revised: April, 2016 MLS Alignment: April, 2017
digits Topic 7: Defining & Comparing Functions
Standard Topic & Section Suggested # of Days
Notes
8.F.A.1 7.1: Recognizing a Function 1
8.F.A.1 7.2: Representing a Function 1
8.F.A.2 7.3: Linear Functions 1
8.F.A.2 7.4: Nonlinear Functions 1
8.F.A.3 7.5: Increasing and Decreasing Intervals
1
8.F.A.1 7.6: Sketching a Function Graph 1
8.F.A.1 8.F.A.2 8.F.A.3
7.6: Problem Solving 1
Review 1.5
Test 1.5
Board Approved: July 23, 2015 14 | Page Revised: April, 2016 MLS Alignment: April, 2017
digits Topic 5: Proportional Relationships, Lines, & Linear Equations
digits Topic 8: Linear Functions
Standard Topic & Section Suggested # of Days
Notes
MA.8.EEI.B.1
5.1: Graphing Proportional Relationships
1 Algebra 4.1-4.3 as needed
8.F.A.2 8.1: Defining a Linear Function Rule
1 Algebra 4.5 as needed
MA.8.EEI.B.2 5.2: Linear Equations y = mx 1 Algebra 4.5-4.6 as needed
8.F.A.2 8.2: Rate of Change 1 Algebra 4.4 as needed
MA.8.EEI.B.1
5.3: Slope of a Line 1 Algebra 4.4 as needed
MA.8.EEI.B.1 5.4: Unit Rates and Slope 1 Algebra 4.4 as needed
8.F.A.2 8.F.A.3
8.3: Initial Value 1 Algebra 4.5 as needed
MA.8.EEI.B.2 5.5: Y-intercept of a Line 1 Algebra 4.5 as needed
MA.8.EEI.B.2 5.6: Linear Equations: y = mx + b
1 Algebra 5.1-5.2 as needed
MA.8.EEI.C.1 8.4: Comparing Two Linear Functions
1
MA.8.EEI.C.1 5.7: Problem Solving 1
8.F.A.2 8.F.A.3
8.6: Problem Solving 1
Topic 8 Review 2
Test Topic 8 2
Board Approved: July 23, 2015 15 | Page Revised: April, 2016 MLS Alignment: April, 2017
digits Topic 6: Systems of Two Linear Equations
Standard Topic & Section Suggested # of Days
Notes
8.EEI.C.2 6.1: What is a System of Linear Equations in Two Variables
2
8.EEI.C.2 6.2: Estimating Solutions of Linear Systems by Inspection
2 Algebra 7.5 as needed
8.EEI.C.2 6.3: Solving Systems of Linear Equations by Graphing
2 Algebra 7.1 as needed
8.EEI.C.2 6.4: Solving Systems of Linear Equations using Substitutions
2 Algebra 7.2 as needed
8.EEI.C.2 6.5: Solving Systems of Linear Equations using Elimination (Addition)
2 Algebra 7.3 as needed
8.EEI.C.2 6.6: Solving Systems of Linear Equations using Elimination (Subtraction)
2 Algebra 7.3 as needed
8.EEI.C.2 Problem Solving 2
Review 2
Test 2
Board Approved: July 23, 2015 16 | Page Revised: April, 2016 MLS Alignment: April, 2017
digits Topic 14: Scatter Plots
Standard Topic & Section Suggested # of Days
Notes
8.DSP.A.1 14.1 Interpreting Scatter Plots 1
8.DSP.A.1 14.2 Constructing Scatter Plots 1
8.DSP.A.1 14.3 Investigating Patterns: Clustering and Outliers
1
8.DSP.A.1 14.4 Investigating Patterns: Association
1
8.DSP.A.2 14.5 Linear Models- Fitting a Straight Lines
1
8.DSP.A.2 14.6 Using the Equation of a Linear Model
1
8.DSP.A.2 14.7 Problem Solving 1
Review 1.5
Topic 4 TEST 1.5
Board Approved: July 23, 2015 17 | Page Revised: April, 2016 MLS Alignment: April, 2017
digits Topic 15: Analyzing Categorical Data *This unit is considered modular, and may be moved to a different time of the
year to accommodate time and testing constraints.
Standard Topic & Section Suggested # of Days
Notes
MA.8.DSP.A.4 15.1: Bivariate Categorical Data 1
MA.8.DSP.A.4 15.2: Constructing Two-way Frequency Tables
1
MA.8.DSP.A.4 15.3: Constructing Two-way Relative Frequency Tables
1
MA.8.DSP.A.4 15.4: Constructing Two-way Relative Frequency Tables
1
MA.8.DSP.A.4 15.5: Interpreting Two-way Relative Frequency Tables
1
MA.8.DSP.A.4 15.6: Choosing a Measure of Frequency 1
MA.8.DSP.A.3 MA.8.DSP.A.4
15.7: Problem Solving 1
Review 1.5
Test 1.5
Board Approved: July 23, 2015 18 | Page Revised: April, 2016 MLS Alignment: April, 2017
Unit 3: Transformations and Transversals Subject: Mathematics Grade: 8th Grade Name of Unit: Transformations and Transversals Length of Unit: 27 Days Overview of Unit: Students will understand the concepts of identifying similar figures and translating those figures on the coordinate plane. Priority Standards for unit:
• MA.8.GM.A.1: Verify experimentally the congruence properties of rigid transformations. a. Verify that angle measure, betweeness, collinearity and distance are preserved
under rigid transformations. b. Investigate if orientation is preserved under rigid transformations.
• MA.8.GM.A.2: Understand that two-dimensional figures are congruent if a series of rigid transformations can be performed to map the pre-image to the image.
a. Describe a possible sequence of rigid transformations between two congruent figures.
• MA.8.GM.A.3: Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.
• MA.8.GM.A.4: Understand that two-dimensional figures are similar if a series of transformations (rotations, reflections, translations and dilations) can be performed to map the pre-image to the image.
a. Describe a possible sequence of transformations between two similar figures. • MA.8.GM.A.5: Explore angle relationships and establish informal arguments.
a. Derive the sum of the interior angles of a triangle. b. Explore the relationship between the interior and exterior angles of a triangle. c. Construct and explore the angles created when parallel lines are cut by a
transversal. d. Use the properties of similar figures to solve problems.
Supporting Standards for unit:
● MA.8.GM.A.1 Verify experimentally the congruence properties of rigid transformations. a. Verify that angle measure, betweeness, collinearity and distance are preserved under
rigid transformations. b. Investigate if orientation is preserved under rigid transformations.
● MA.8.GM.A.2 Understand that two-dimensional figures are congruent if a series of rigid transformations can be performed to map the pre-image to the image.
● MA.8.GM.A.4 Understand that two-dimensional figures are similar if a series of transformations (rotations, reflections, translations and dilations) can be performed to map the pre-image to the image.
Board Approved: July 23, 2015 19 | Page Revised: April, 2016 MLS Alignment: April, 2017
● ISTE-EMPOWERED LEARNER 1: Students leverage technology to take an active role in choosing, achieving and demonstrating competency in their learning goals, informed by the learning sciences.
● ISTE-KNOWLEDGE COLLECTOR.3: Students critically curate a variety of resources using digital tools to construct knowledge, produce creative artifacts and make meaningful learning experiences for themselves and others.
● ISTE-COMPUTATIONAL THINKER.5: Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions.
Standards
Unwrapped Concepts (Students need to
know)
Unwrapped Skills (Students need to
be able to do) Bloom’s
Taxonomy Levels Webb's DOK
MA.8.GM.A.4
two-dimensional figures are similar if a series of
transformations (rotations, reflections,
translations and dilations) can be
performed to map the pre-image to the image. Understand Understand 2
MA.8.GM.A.4
possible sequence of transformations between
two similar figures. Describe Understand 2
MA.8.GM.A.5
angle relationships and establish informal
arguments. Explore Understand 3
MA.8.GM.A.5 sum of the interior angles of a triangle. Derive Create 2
MA.8.GM.A.5
relationship between the interior and exterior angles of a triangle Explore Understand 3
MA.8.GM.A.5
the angles created when parallel lines are cut by a
transversal Explore Understand 3
MA.8.GM.A.5
properties of similar figures to solve
problems. Use Analyze 2
Board Approved: July 23, 2015 20 | Page Revised: April, 2016 MLS Alignment: April, 2017
Essential Questions: 1. What does it mean for two figures to be identical? 2. How do geometric properties and logical reasoning allow you to form arguments and
make conclusions about relationships in geometry? Enduring Understanding/Big Ideas:
1. Two figures are identical if you can map one to the other by a sequence of rigid motions, such as translations, reflections, and rotations.
2. You can use what you know about transversals, parallel lines, and Pythagorean Theorem to identify, compare, or contrast geometric shapes.
Unit Vocabulary:
Academic Cross-Curricular Words Content/Domain Specific
Flip Turn Slide
Enlarge Shrink
Increase Decrease
Similar
Corresponding Interior Exterior
Topic 9 Congruent Figures
Image Reflection
Rigid Motion Rotation
Transformation Translation
Topic 10 Dilation
Enlargement Reduction
Scale Factor Similar Figures
Topic 11
Alternate Interior Angles Corresponding Angles Deductive reasoning
Exterior angle of a triangle Transversal
Resources for Vocabulary Development: Use quality tools (See Adult Learning Framework handbook)
Board Approved: July 23, 2015 21 | Page Revised: April, 2016 MLS Alignment: April, 2017
digits Topic 9: Congruence
Standard Topic & Section Suggested # of Days
Notes
MA.8.GM.A.1 9.1: Translations 1
MA.8.GM.A.1 9.2: Reflections 1
MA.8.GM.A.1 9.3: Rotations 1
MA.8.GM.A.1 9.1 - 9.3 Review 1
9.1 - 9.3 QUIZ 1
MA.8.GM.A.2 9.4: Congruent Figures 1
MA.8.GM.A.1 MA.8.GM.A.2
9.5: Problem Solving 1
Review 2
Topic 9 TEST 1
Board Approved: July 23, 2015 22 | Page Revised: April, 2016 MLS Alignment: April, 2017
digits Topic 10: Similarity
Standard Topic & Section Suggested # of Days
Notes
MA.8.GM.A.3 10.1: Dilations 1
MA.8.GM.A.4 10.2: Similar Figures 1
MA.8.GM.A.4 10.3: Relating Similar Triangles and Slope
1
MA.8.GM.A.3 MA.8.GM.A.4
10.4: Problem Solving 1
Board Approved: July 23, 2015 23 | Page Revised: April, 2016 MLS Alignment: April, 2017
digits Topic 11: Reasoning in Geometry
Standard Topic & Section Suggested # of Days
Notes
MA.8.GM.A.5 11.1: Angles, Lines and Transversals
1
MA.8.GM.A.5 11.2: Reasoning and Parallel Lines
1
MA.8.GM.A.5 11.3: Interior Angles of Triangles
1
MA.8.GM.A.5 11.4: Exterior Angles of Triangles
1
MA.8.GM.A.5 11.5: Angle to Angle Triangle Similarity
1
MA.8.GM.A.5 11.6 Problem Solving 1
Review 2
Test Topic 11 1
Board Approved: July 23, 2015 24 | Page Revised: April, 2016 MLS Alignment: April, 2017
Unit 4: Exponential Functions, Pythagorean Theorem and Volume
Subject: Mathematics Grade: 8th Grade Name of Unit: Exponential Functions, Pythagorean Theorem and Volume Length of Unit: 35 Days Overview of Unit: Students will work with radicals and integer exponents and understand the concepts of geometric reasoning as it relates to the Pythagorean Theorem. Students will also solve real-world and mathematical problems involving volume. Priority Standards for unit:
● MA.8.GM.B.1 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
● MA.8.GM.C.1 Solve problems involving volume of cones, pyramids and spheres. ● MA.8.EEI.A.1 Know and apply the properties of integer exponents to generate equivalent
numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27. Supporting Standards for unit:
● MA.8.GM.B.1 Explain a proof of the Pythagorean Theorem and its converse. ● MA.8.GM.B.3 Apply the Pythagorean Theorem to find the distance between two points
in a coordinate system. ● MA.8.GM.C.1 Solve problems involving surface area and volume.
a. Understand the concept of surface area and find surface area of pyramids. b. Understand the concepts of volume and find the volume of pyramids, cones
and spheres. ● MA.8.EEI.A.2 Solve equations of the form x2 = p and x3 = p, where p is a positive
rational number. ● MA.8.EEI.A.2 Evaluate square roots of perfect squares less than or equal to 625 and cube
roots of perfect cubes less than or equal to 1000. ● MA.8.EEI.A.2 Recognize that square roots of non-perfect squares are irrational. ● MA.8.EEI.A.4: Use scientific notation to solve problems.
a. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.
b. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.
● ISTE-EMPOWERED LEARNER 1: Students leverage technology to take an active role in choosing, achieving and demonstrating competency in their learning goals, informed by the learning sciences.
Board Approved: July 23, 2015 25 | Page Revised: April, 2016 MLS Alignment: April, 2017
● ISTE-KNOWLEDGE COLLECTOR.3: Students critically curate a variety of resources using digital tools to construct knowledge, produce creative artifacts and make meaningful learning experiences for themselves and others.
● ISTE-INNOVATIVE DESIGNER.4: Students use a variety of technologies within a design process to identify and solve problems by creating new, useful or imaginative solutions.
● ISTE-COMPUTATIONAL THINKER.5: Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions.
Standards Unwrapped Concepts
(Students need to know)
Unwrapped Skills (Students need to
be able to do) Bloom’s
Taxonomy Levels Webb's DOK
MA.8.EEI.A.1
the properties of integer exponents to generate equivalent numerical
expressions Know Remember 1
MA.8.EEI.A.1
the properties of integer exponents to generate equivalent numerical
expressions Apply Apply 2
A.8.GM.B.1
models to demonstrate a proof of the Pythagorean Theorem
and its converse Use Apply 2
MA.8.GM.B.2
the Pythagorean Theorem to determine unknown side
lengths in right triangles in problems in two- and three-
dimensional contexts. Use Apply 2
A.8.GM.C.1 problems involving surface
area and volume. Solve Apply 2
MA.8.EEI.A.4
scientific notation and choose units of appropriate size for
measurements of very large or very small quantities. Use Apply
2
MA.8.EEI.A.4
scientific notation and choose units of appropriate size for
measurements of very large or very small quantities. Use Apply 2
Board Approved: July 23, 2015 26 | Page Revised: April, 2016 MLS Alignment: April, 2017
Essential Questions: 1. How do geometric properties and logical reasoning allow you to form arguments and
make conclusions about relationships in geometry? 2. Measurements frequently involve very large or very small numbers. How can you make
such measurements easy to use and compare? 3. How can you tell whether a linear equation models a proportional relationship? 4. What methods can you use to solve pairs of simultaneous linear equations in two
variables? Enduring Understanding/Big Ideas:
1. You can use what you know about Pythagorean Theorem to identify, compare, or contrast geometric shapes.
2. The process of scientific notation can be used to work with and express extreme values. 3. Understanding the forms of linear equations such as y = mx + b can give you the ability
to determine the type of line presented in equation form. 4. You may use graphing, substitution or elimination to determine if a solution exists and
then to find the solution to set of equations. Unit Vocabulary:
Academic Cross-Curricular Words Content/Domain Specific
Topic 3 Cube Root
Negative Exponent Property Perfect Cube
Zero Exponent Property
Topic 4 Scientific Notation
Topic 12
Proof Theorem
Hypotenuse Leg of a Right Triangle Pythagorean Theorem
Converse of Pythagorean Theorem
Topic 13 Base Cone
Cylinder Height
Board Approved: July 23, 2015 27 | Page Revised: April, 2016 MLS Alignment: April, 2017
Lateral Area Lateral Surface
Radius Right Cone
Right Cylinder Slant Height
Sphere Surface Area
Vertex Volume
Resources for Vocabulary Development: Use quality tools (See Adult Learning Framework handbook)
Board Approved: July 23, 2015 28 | Page Revised: April, 2016 MLS Alignment: April, 2017
digits Topic 3: Integer Exponents
Standard Topic & Section Suggested # of Days
Notes
MA.8.EEI.A.2 3.1: Perfect Squares, Square Roots, and Equations of the form x2 = p
1
MA.8.EEI.A.1 3.2: Perfect Cubes, Cube Roots, and Equations of the form x3 = p
1
MA.8.EEI.A.1 3.3: Exponents and Multiplication 1
MA.8.EEI.A.1 3.4: Exponents and Division 1
MA.8.EEI.A.1 3.5: Zero and Negative Exponents 1
MA.8.EEI.A.1 3.6: Comparing Expressions with Exponents
1
MA.8.EEI.A.1 3.7: Problem Solving 1
Review Topic 3 1.5
TEST Topic 3 1.5
Board Approved: July 23, 2015 29 | Page Revised: April, 2016 MLS Alignment: April, 2017
digits Topic 12: Using the Pythagorean Theorem
Standard Topic & Section Suggested # of Days
Notes
MA.8.GM.B.1 12.1: Reasoning and Proof 1
MA.8.GM.B.1 MA.8.GM.B.2
12.2: Pythagorean Theorem 1
MA.8.GM.B.2 MA.8.EEI.A.1
12.3: Finding Unknown Leg Lengths
1
MA.8.GM.B.1 12.4: Converse of Pythagorean Theorem
1
MA.8.GM.B.3 12.5: Distance in the Coordinate Plane
1
MA.8.GM.B.1 MA.8.GM.B.2
12.6: Problem Solving 2
Review 1.5
Topic 12 TEST 1.5
Board Approved: July 23, 2015 30 | Page Revised: April, 2016 MLS Alignment: April, 2017
digits Topic 13: Surface Area and Volume
Standard Topic & Section Suggested # of Days
Notes
A.8.GM.C.1 13.2: Volume of Cylinders 1
A.8.GM.C.1 13.4: Volume of Cones 1
A.8.GM.C.1 13.6: Volume of Spheres 1
A.8.GM.C.1 13.7: Problem Solving 1
Review 1.5
Topic 13 QUIZ 1.5
Board Approved: July 23, 2015 31 | Page Revised: April, 2016 MLS Alignment: April, 2017
digits Topic 4: Scientific Notation
Standard Topic & Section Suggested # of Days
Notes
MA.8.EEI.A.3 4.1 Exploring Scientific Notation 1
MA.8.EEI.A.3 4.2 Using Scientific Notation to Describe Very Large Quantities
1
MA.8.EEI.A.3 4.3 Using Scientific Notation to Describe Very Small Quantities
1
MA.8.EEI.A.3 4.4 Operating with Numbers Expressed in Scientific Notation
1
MA.8.EEI.A.3 MA.8.EEI.A.4
4.5 Problem Solving 1
Review 1.5
Topic 4 TEST 1.5
Board Approved: July 23, 2015 32 | Page Revised: April, 2016 MLS Alignment: April, 2017
Unit of Study Terminology Appendices: All Appendices and supporting material can be found in this course’s shell course in the District’s Learning Management System. Assessment Leveling Guide: A tool to use when writing assessments in order to maintain the appropriate level of rigor that matches the standard. Big Ideas/Enduring Understandings: Foundational understandings teachers want students to be able to discover and state in their own words by the end of the unit of study. These are answers to the essential questions. Engaging Experience: Each topic is broken into a list of engaging experiences for students. These experiences are aligned to priority and supporting standards, thus stating what students should be able to do. An example of an engaging experience is provided in the description, but a teacher has the autonomy to substitute one of their own that aligns to the level of rigor stated in the standards. Engaging Scenario: This is a culminating activity in which students are given a role, situation, challenge, audience, and a product or performance is specified. Each unit contains an example of an engaging scenario, but a teacher has the ability to substitute with the same intent in mind. Essential Questions: Engaging, open-ended questions that teachers can use to engage students in the learning. Priority Standards: What every student should know and be able to do. These were chosen because of their necessity for success in the next course, the state assessment, and life. Supporting Standards: Additional standards that support the learning within the unit. Topic: These are the main teaching points for the unit. Units can have anywhere from one topic to many, depending on the depth of the unit. Unit of Study: Series of learning experiences/related assessments based on designated priority standards and related supporting standards. Unit Vocabulary: Words students will encounter within the unit that are essential to understanding. Academic Cross-Curricular words (also called Tier 2 words) are those that can be found in multiple content areas, not just this one. Content/Domain Specific vocabulary words are those found specifically within the content. Symbols: This symbol depicts an experience that can be used to assess a student’s 21st Century Skills using the rubric provided by the district. This symbol depicts an experience that integrates professional skills, the development of professional communication, and/or the use of professional mentorships in authentic classroom learning activities.